Supergravity and the jet quenching parameter in the presence of R-charge densities

TL;DR

The paper studies how finite R-charge densities affect jet quenching in ${\cal N}=4$ SYM by computing $\hat{q}$ using AdS/CFT with non-extremal rotating D3-branes. The authors derive a general spacelike-string prescription for $\hat{q}$ in these backgrounds and analyze two representative spin configurations (two equal angular momenta and one nonzero angular momentum) in both canonical and grand canonical ensembles. They find that R-charges generally enhance jet quenching, with the degree and pattern of enhancement depending on the number of independent angular momenta and the ensemble. The results provide a controlled, nonperturbative look at how chemical potentials and R-charges influence parton energy loss in strongly coupled plasmas, and connect to related drag-force analyses in the literature.

Abstract

Following a recent proposal, we employ the AdS/CFT correspondence to compute the jet quenching parameter for N=4 Yang-Mills theory at nonzero R-charge densities. Using as dual supergravity backgrounds non-extremal rotating branes, we find that the presence of the R-charges generically enhances the jet quenching phenomenon. However, at fixed temperature, this enhancement might or might not be a monotonically increasing function of the R-charge density and depends on the number of independent angular momenta describing the solution. We perform our analysis for the canonical as well as for the grand canonical ensemble which give qualitatively similar results.

Figures (2)

• Figure 1: The $\hat{q} / \hat{q}_0$ ratio for the case of two equal nonzero angular parameters plotted as a function of the dimensionless parameter $0\leqslant \xi<\infty$ in (\ref{['3-18']}) appropriate for the CE. Some indicative values are: $(\xi, {\hat{q}\over \hat{q}_0}) = ({1\over 2}, 1.04), (1, 1.15)$ and $(3,1.76)$. The corresponding plot for the GCE in terms of the parameter $0\leqslant \hat{\xi}\leqslant 1$ in (\ref{['fhi2']}) is similar in shape with indicative values $(\hat{\xi}, {\hat{q}\over \hat{q}_0}) = ({1\over 2}, 1.33)$ and $(1, 2.43)$.
• Figure 2: The $\hat{q} / \hat{q}_0$ ratio for the case of one nonzero angular parameter and the CE plotted as a function of the dimensionless parameter $0\leqslant \xi\leqslant \xi_{\rm max}$ in (\ref{['xidef']}). The maximum and final values occurring at $\xi_0 = 1.09$ and $\xi_{\rm max}=1.33$ are ${\hat{q}\over \hat{q}_0}= 1.37$ and $1.19$, respectively. The corresponding plot for the GCE in terms of the parameter $0\leqslant \hat{\xi}\leqslant {1\over 2}$ in (\ref{['ol1']}) is similar in shape. The maximum and final values occurring at $\hat{\xi}_0 = 0.499$ and $\hat{\xi}_{\rm max}={1\over 2}$, are ${\hat{q}\over \hat{q}_0}= 1.369$ and $1.368$, respectively. Note the closeness of the maximum and final values in the GCE case.